Superfluid Friction and Late-time Thermal Evolution of Neutron Stars

The recent temperature measurements of the two older isolated neutron stars PSR 1929+10 and PSR 0950+08 (ages of $3\times 10^6$ and $2\times 10^7$ yr, respectively) indicate that these objects are heated. A promising candidate heat source is friction between the neutron star crust and the superfluid it is thought to contain. We study the effects of superfluid friction on the long-term thermal and rotational evolution of a neutron star. Differential rotation velocities between the superfluid and the crust (averaged over the inner crust moment of inertia) of $\bar\omega\sim 0.6$ rad s$^{-1}$ for PSR 1929+10 and $\sim 0.02$ rad s$^{-1}$ for PSR 0950+08 would account for their observed temperatures. These differential velocities could be sustained by pinning of superfluid vortices to the inner crust lattice with strengths of $\sim$ 1 MeV per nucleus. Pinned vortices can creep outward through thermal fluctuations or quantum tunneling. For thermally-activated creep, the coupling between the superfluid and crust is highly sensitive to temperature. If pinning maintains large differential rotation ($\sim 10$ rad s$^{-1}$), a feedback instability could occur in stars younger than $\sim 10^5$ yr causing oscillations of the temperature and spin-down rate over a period of $\sim 0.3 t_{\rm age}$. For stars older than $\sim 10^6$ yr, however, vortex creep occurs through quantum tunneling, and the creep velocity is too insensitive to temperature for a thermal-rotational instability to occur. These older stars could be heated through a steady process of superfluid friction.